Steel wires coated with a metal layer are widely known. Tonnages of steel wires have been coated with a zinc or zinc alloy layer in order to increase the corrosion resistance of steel wires. The corrosion resistance of these steel wires is largely dependent upon the thickness of the zinc layer. The thicker the zinc layer, the longer it takes before it is corroded away and the higher the corrosion resistance, and vice versa. In some cases these steel wires with a zinc layer exhibit surface defects. These surface defects may take several forms: impurities, rests of lubricants such as drawing soaps remaining at the surface, hard Fe—Zn particles, burrs, rolling errors, drawing lines, asperities, and so forth. Dependent upon the eventual use of the steel wires, these surface defects may have various drawbacks. A first drawback is that the visual or esthetic aspect of the steel wire with the metal layer is bad due to inhomogenities. A second drawback is that the surface errors may lead to peaks, which may pierce through subsequently applied thin or soft layers such as a lacquer layer or a plastic layer. A third drawback is that asperities on the surface of the metal coated steel wire may cause damage to other devices, which are or which come in contact with the steel wires. Equalizing the surface of the metal layer, e.g. by etching, in order to get rid of the surface defects, unavoidably decreases the thickness of the metal layer. In case of a zinc or zinc alloy layer, this decreased thickness means a reduced corrosion resistance. In order to have a final corrosion resistance, which meets minimum requirements, an initial thicker layer must be deposited.